3x-7=2x^2-15x+33

Solution for 3x-7=2x^2-15x+33 equation:

3x-7=2x^2-15x+33

We move all terms to the left:

3x-7-(2x^2-15x+33)=0

We get rid of parentheses

-2x^2+3x+15x-33-7=0

We add all the numbers together, and all the variables

-2x^2+18x-40=0

a = -2; b = 18; c = -40;
Δ = b2-4ac
Δ = 182-4·(-2)·(-40)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2}{2*-2}=\frac{-16}{-4}
=+4
$